Forward Physics – Appendix for Annual Report 2014

Forward Physics – Appendix for Annual Report 2014

For the single-top quark analysis at CDF, events with the following characteristics were selected: a lepton (either an electron or a muon) with high transverse energy, a large imbalance of transverse momentum, which indicates the presence of a neutrino, and two or three jets, at least one of which must originate from a bottom quark.1

By using artificial neural networks in the analysis, a single-top quark cross section of 3.04 +0.57/-0.53 picobarns was measured (Figure 1).

Figure 1: Results of the two-dimensional fit for σ(s) and σ(t+Wt). The black circle shows the best-fit value, and the 68.3%, 95.5% and 99.7% confidence regions are shown as shaded areas. The Standard Model (SM) predictions are also included with their theoretical uncertainties.

Searching for boosted tops

When the jets are Lorentz-boosted into a jet-jet center-of-mass system, the ones representing primary light quarks are expected to have a lower mass, and can be used for added background discrimination. In Figure 2 below, the measured effective mass of a jet is plotted against the mass of another one belonging to the selected pair of jets. A pair of jets for which each individual jet has a mass between 40 and 60 GeV/c2 dominate. The measured masses are consistent with the predictions of Quantum Chromodynamics (QCD).2

In case the high mass jet-jet pairs originate from a decay of a top quark (with the measured mass of 173.34 ± 0.76 GeV/c2) a cluster of events in which both jets have masses between 140 and 200 GeV/c2 is expected (see Figure 2). Although there are roughly 30 such events in the data, it is only slightly more than is expected from an unlikely production of two very massive jets by the light quarks.

The data was used to set an upper limit for the rate of top quarks being produced at these very high energies of 40 femtobarns, i.e., they were produced in less than in a single collision in every trillion events. This is to be compared to the Standard Model expectation of top quark production exhibiting two jets of 5 femtobarns.

In 2014, the lepton asymmetry measurement was completed by using the full Tevatron Run II data sample with two charged leptons from top pair decays. The resulting asymmetry in the two-lepton mode (Figure 3) was measured to be 7.2 ± 6.0%.3

After combining this with the previous measurement, based on the data with only one charged lepton from top pair decays, the final CDF measurement of this asymmetry was 9.0 +2.8/-2.6% (see lower figure). While there are several competing theoretical predictions for the asymmetry, the most current theoretical prediction is 4%.

The new result has a high impact for the top quark studies and places further constraints on the QCD predictions. The CDF analyses will continue, particularly in studies of the asymmetry of the top quark pairs in the two-lepton mode. Measurements of the asymmetry of the bottom quark pairs that probe the same physics question are also on the way.

Figure 3. A comparison of forward-backward asymmetry measured in this experiment (DIL, dilepton mode), in an earlier CDF measurement in one-lepton mode (L+J, lepton + jets), and in their combination.

Is the top hiding a charged Higgs?

According to the Standard Model, the heaviest of the six quarks – the top quark – decays into a charged lepton, a neutrino and a bottom quark (Figure 4). In most analyses at the Tevatron and in the LHC experiments, this decay involves an intermediate W boson. The W boson decays into either an electron or a muon (accompanied with their unseen neutrinos) are selected in these analyses.

The W boson can also decay into the tau lepton, which is heavier than an electron or a muon. (see figure below). The tau lepton decay channel is less explored than the other two because it is more challenging to identify. After the tau lepton decays in the detector, the CDF level 1 track trigger — instrumentation that helps with the rapid selection of important events among the hundreds of trillions that occur inside the detector — selects the tau leptons. Finally, offline software reconstructs the tau from its fragments.

The W boson is not the only particle that could decay into a tau. Certain new particles, like additional Higgs bosons, could provide further decay channels with a preference for heavy particles, including taus.

A top quark, then — through either a W boson or a new particle such as a Higgs — decays into a tau lepton, a tau neutrino, and a bottom quark. Analysing this decay channel will help scientists assess the effects of new physics.

CDF measures the number of taus produced from top-antitop pairs. The number is the product of the production of top-antitop pairs, called the cross section, and the fraction of the pairs that decay into taus, called the branching fraction. New physics could modify either rate, so when evidence of new physics is seen, it is not obvious which of the two is affected. With two unknowns, a single equation will not help to solve the problem, a second equation using a second set of data is needed.

This CDF analysis separates – for the first time – single-tau from two-tau events to effectively get the second equation for the two unknowns. We can then measure the branching fraction of the top quark into a tau lepton independently of the cross section.4

The result is that the branching fraction for a top quark into a tau lepton, a tau neutrino and a bottom quark is 9.6 ± 2.8%, which is in agreement with the Standard Model.

This measurement, which depends on our understanding of the upper figure, can be used to calculate the branching fraction shown in the lower figure.

A branching fraction of a top quark into a charged Higgs boson is excluded (in the mass range from 80 to 140 GeV/c2) and a bottom quark at the 5.9 percent level. The exclusion is at the 95% confidence level and is comparable with recent measurements at the LHC.

Figure 4. The Feynman diagram depicting production and decay of a top-antitop pair. In the upper part, the top quark decays into a W+ and an anti-b quark. The W+ then decays into a tau lepton and a neutrino.

The top, the bottom and everything in between

In collisions of high-energy beams, new, heavy particles are usually produced in pairs: a matching antiparticle for every particle. This is the case for the bottom quark and the top quark, both discovered at Fermilab. But every now and then, the weak force is responsible for the collision, and so particles can be transmuted from one kind into another (see Figure 5). The weak interaction can also produce a pair of dissimilar particles, a bit like giving birth to fraternal twins rather than identical ones. Studying the rate of such production tells us volumes about the secrets of the weak force and possible new interactions that may mimic it, especially if they favor heavy particles such as the top quark.

This measurement describes a search for such a process: a top quark and an associated anti-bottom quark are produced via s-channel W boson exchange (see figure below). It is similar to an earlier reported study on evidence for the s-channel process used in a search in what is known as the lepton-plus-jets mode.5

The search described in this column is performed in the so-called missing-energy-plus-jets mode. The production mechanism is the same as the earlier CDF search — the top quark decays to a W boson and a bottom quark, and the W boson subsequently decays to a lepton and a neutrino. The two bottom quarks, circled in green in the above figure, produce jets that have long-lived, heavy B hadrons in them. If the lepton is not identified, we use it in the missing-energy-plus-jets analysis; otherwise the earlier analysis makes use of it.

One challenge of analysing data with jets and missing energy is that they can be mimicked by events with only jets in them. These jets-only events can be mismeasured, resulting in large amounts of fake missing energy. Some of these mismeasured events then contaminate the sample of events used to search for the single-top signal. Scientists use sophisticated algorithms to reduce the amount of contamination from these events, and then use the rejected data to estimate the amount that remains. Other algorithms reduce the contamination from other sources.

The measured cross section in this analysis is 1.12 +0.61/-0.57 picobarns. When combined with the earlier lepton-plus-jets result, the cross section is 1.36 +0.37/-0.32 picobarns. The addition of the missing-energy analysis increases the sensitivity of the combination by more than 10 percent compared with the lepton-plus-jets result alone. This analysis forms the CDF contribution to the Tevatron combined observation of the s-channel single top quark process.

Figure 5. The diagram depicting the s-channel single-top quark production mechanism searched for in the analysis; the process selects signal events in which the lepton is not identified.

CDF documentation for the W boson mass measurement

In Tevatron Run I (1990), 1 722 W-boson events were used to obtain the W boson mass of 79 910 ± 390 MeV/c2. Between Run I and Run II, all of the tracking chambers were rebuilt in order to improve accuracy. A new measurement was based on more than 60 times the number of W boson events in 1990, and brought the mass uncertainty down to 390 MeV/c2. The W mass was now measured to be 80 413 ± 48 MeV/c2 based on 115 092 events. This was the world’s single most precise measurement of the W mass. For the 2012 measurement, the goal was to reduce the 48 MeV/c2 uncertainty below the previous world average of 23 MeV/c2.

The largest single systematic uncertainty in this measurement, ± 23 MeV/c2, was due the uncertainty in the calibration of the momentum of the decay electron and muon. The collaboration improved the calibration of the electron energy scale using, in decays of both the W and the Z boson, the ratio of its energy to its momentum. This calibration technique was validated by applying it to the measurement of the mass of the Z boson decaying into two electrons; the momentum calibration was verified by using the J/ψ- and Υ-to-muon pair decays and cross-checked by using the Z-to-muon pair mass measurement. In the current measurement, the uncertainty of the electron and muon energy scale is reduced to ± 7 MeV/c2.

The 2012 measurement of the W boson mass by the CDF experiment, 80 387 ± 19 MeV/c2, was based on 470 126 candidates in which a W decays into an electron and a neutrino, and on 624 708 candidates in which a W decays into a muon and a neutrino. The combined world average now yielded a W boson mass of 80 385 ± 15 MeV/c2 (Table 1).

What has changed since February 2012? The Higgs boson has been discovered, and its mass has been determined to a high accuracy, allowing a prediction of the W boson mass of 80 359 ± 11 MeV/c2. The comparison of this prediction with the combined world average places bounds on non-Standard Model physics.6

Table 1. Uncertainties in units of MeV/c2 in the latest result for the mass of the W boson, which was determined to be 80 387 ± 19 MeV/c2. The total uncertainty amounts to 0.02%.

An improved search for a dijet resonance

The CDF collaboration recently reported another study of collisions giving rise to a W or Z boson and two quarks (jets).7 The data were purposefully selected to be completely independent of the data that gave rise to the excess in the earlier study. The original data set required a lepton with a high transverse momentum; the current analysis vetoes any event with a high-transverse-momentum lepton. The idea was to cross-check earlier results and, at the same time, to probe the scenario in which the hypothetical new particle would truly exist and would also appear together with a Z boson, as suggested by several scientists. In the 2014 analysis, additional corrections to reconstructed jets in simulated events were applied. These corrections more accurately model particle showers that are initiated by both quarks and gluons.

The original selection resulted in more than 2 million events. The principal background is multi-jet events, which are produced by the strong interaction. After using up-to-date analysis tools, the number of multi-jets was reduced to 6 280 ± 1 190 (see above figure). The experiment found 2 900 ± 183 diboson events (WW, WZ, ZZ). This number of diboson events translates into a measured cross section of 13.8 +3.0/-2.7 picobarns. This number is in agreement with the Standard Model value of 16.8 ± 1.0.

The most important result of this analysis is that no anomalies (no second peaks) are observed in the dijet mass spectrum (Figure 6). This story summarises beautifully many of the salient features of the scientific journey: the appearance of an experimental anomaly in a well-established framework, leading to great excitement; the process of independently checking the validity of the result; and finally the improved understanding of nature that inherently follows either its confirmation or disproval. Here, what appeared to be a potential game changer to particle physics ended up producing a sounder understanding of important physics processes.

This search looked for the production of three leptons plus missing energy and is characterized by three well-understood backgrounds. The lepton class of particles comprises electrons, muons and taus.8

CDF analysts studied extensively all backgrounds, both in counting and kinematics, in a large number of dilepton and trilepton control regions before they were convinced they understood the Standard Model as it manifests itself in multilepton final states. They did not allow themselves to look at the signal region before this process was fully concluded, making this a “blind” search for new physics.

The final step was to uncover the signal region and study the observed events. The two highest-energy leptons must be an electron or a muon, while the lowest-energy lepton can be an electron, a muon or a tau. An excess of trilepton events was observed at low dilepton mass. Scientists observed 34 electron pairs with a third lepton when only 20 ± 4 were expected. They also observed 19 muon pairs with a third lepton when 13 ± 2 were expected. The results are displayed in Figure 7.

The probability that such an excess over the same energy range (between 10 and 85 GeV/c2) was produced by a statistical fluctuation from background events anywhere in the spectrum is 3.2% (1.85 sigma effect), which is not threatening to the Standard Model. Although new physics was not observed, the understanding of Standard Model multileptonic processes at CDF reached an unprecedented level, which could stimulate new searches for even more unexpected signals.

Figure 7. The dilepton mass distribution of electron- or muon-pair + lepton events for the Standard Model background, CDF data and a SUSY benchmark (stacked on top of the Standard Model background) in the signal region.